Optimal Power Flow By Newton Approach

ESCA Corporation
IEEE Transactions on Power Apparatus and Systems 11/1984; 103(10):2864 - 2880. DOI: 10.1109/TPAS.1984.318284
Source: IEEE Xplore


The classical optimal power flow problem with a nonseparable objective function can be solved by an explicit Newton approach. Efficient, robust solutions can be obtained for problems of any practical size or kind. Solution effort is approximately proportional to network size, and is relatively independent of the number of controls or binding inequalities. The key idea is a direct simultaneous solution for all of the unknowns in the Lagrangian function on each iteration. Each iteration minimizes a quadratic approximation of the Lagrangian. For any given set of binding constraints the process converges to the Kuhn-Tucker conditions in a few iterations. The challenge in algorithm development is to efficiently identify the binding inequalities.

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    • "It consists in determining the operating point of controllable resources in an electric network in order to satisfy a specific network objective subject to a wide range of constraints. Typical controllable resources considered in the literature are generators, storage systems, on-load tap changers (OLTC), flexible AC transmission systems (FACTS) and loads (e.g., [4]–[8]). The network objective is usually the minimization of losses or generation costs, and typical "
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    ABSTRACT: The optimal power-flow problem (OPF) has always played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations that render the problem convex, but that consequently yield inexact solutions. Recently, Farivar and Low proposed a method that is claimed to be exact for the case of radial distribution systems, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines' current flows and, on the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions related to the unboundedness of specific control variables. Recently, several contributions have proposed OPF algorithms that rely on the use of the alternating-direction method of multipliers (ADMM). However, as we show in this work, there are cases for which the ADMM-based solution of the non-relaxed OPF problem fails to converge. To overcome the aforementioned limitations, we propose a specific algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems that is based on the method of multipliers, as well as on a primal decomposition of the OPF problem. In view of the complexity of the contribution, this work is divided in two parts. In Part I, we specifically discuss the limitations of both BFM and ADMM to solve the OPF problem. In Part II, we provide a centralized version, as well as a distributed asynchronous version of the proposed OPF algorithm and we evaluate its performances using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder.
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    • "The earlier researches are done in different methods of optimal power flow. The methods are Linear Programming in [1], Nonlinear Programming in [2], Quadratically convergent in [3], Newton approach in [4], Interior Point Method in [5] [6] and P-Q decomposition in [7]. "
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    ABSTRACT: The optimization is an important role in wide geographical distribution of electrical power market, finding the optimum solution for the operation and design of power systems has become a necessity with the increasing cost of raw materials, depleting energy resources and the ever growing demand for electrical energy. In this paper, the real coded biogeography based optimization is proposed to minimize the operating cost with optimal setting of equality and inequality constraints of thermal power system. The proposed technique aims to improve the real coded searing ability, unravel the prematurity of solution and enhance the population assortment of the biogeography based optimization algorithm by using adaptive Gaussian mutation. This algorithm is demonstrated on the standard IEEE-30 bus system and the comparative results are made with existing population based methods.
    Journal of Electrical Engineering and Technology 01/2015; 10(1):56-63. DOI:10.5370/JEET.2015.10.1.056 · 0.53 Impact Factor
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    • "Several analytical as well as developmental classical methods have been used so far in the literature to solve the OPF problem, such as nonlinear programming (NLP) [1], linear programming (LP) [1] [2], gradient based method [3], quadratic programming (QP) [4], Newton-based method [5] [6] and interior point (IP) methods [7]. However, from the literature, it can be concluded that, these techniques could not solve the complex objective functions which are not differentiable, mostly with complicated constraints. "
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    ABSTRACT: This article presents application of nondominated sorting multi objective gravitational search algorithm (NSMOGSA) for solution of different optimal power flow (OPF) problems. In NSMOGSA, the gravitational acceleration of the original gravitational search algorithm (GSA) is updated using a nondominated sorting concept. Fast elitist nondominated sorting and crowding distance have been used to locate and manage the Pareto optimal front. An external archive of the Pareto optimal solutions are also used to provide some elitism. The proposed method is employed for optimal adjustments of the power system control variables which involve continuous variables of the OPF problem. The efficacy of NSMOGSA has been tested on IEEE 30-bus system with four different objectives that reflect minimization of active power loss, total fuel cost, bus voltage deviation and enhancement of voltage stability. Simulation results are also compared with the results found by other techniques reported in the recent literature to show the algorithmic efficacy of NSMOGSA. The obtained results using NSMOGSA has also been tested on some standard benchmark functions to evaluate its potential. Numerical results reveal the tangible superiority of the proposed method in achieving the optimum solution.
    International Journal of Electrical Power & Energy Systems 11/2014; 62:323–334. DOI:10.1016/j.ijepes.2014.04.053 · 3.43 Impact Factor
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